Question

[Kim Tuyền]

Lg²x - logx.log₂(4x)+2log₂x=0 . Tổng nghiệm là bao nhiêu

Answer 1

[Nguyễn Việt Lâm]

Đề như vậy hả bạn?

\(log^2x-logx.log_2\left(4x\right)+2log_2x=0\)

\(\Leftrightarrow log^2x-logx.\left(log_24+log_2x\right)+2log_2x=0\)

\(\Leftrightarrow log^2x-logx.\left(2+log_2x\right)+2log_2x=0\)

\(\Leftrightarrow log^2x-2logx-logx.log_2x+2log_2x=0\)

\(\Leftrightarrow logx\left(logx-2\right)-log_2x\left(logx-2\right)=0\)

\(\Leftrightarrow\left(logx-2\right)\left(logx-log_2x\right)=0\) \(\Rightarrow\left[{}\begin{matrix}logx=2\Rightarrow x=100\\logx-log_2x=0\left(1\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow logx-\dfrac{logx}{log2}=0\Rightarrow logx\left(1-\dfrac{1}{log2}\right)=0\Rightarrow logx=0\Rightarrow x=1\)

Vậy tổng các nghiệm là \(100+1=101\)